生成雅可比方程的弱解

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-01-01 DOI:10.3934/mine.2023064

F. Jiang

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引用次数: 1

摘要

在生成函数和域的适当假设下，证明了生成的雅可比方程弱解的两组关系，分别是最优运输情况和标准monge - amp情况的推广。一类弱溶液是Aleksandrov溶液、Brenier溶液和C -粘度溶液。另一类弱溶液是Trudinger溶液和L^p -粘度溶液。

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Weak solutions of generated Jacobian equations

We prove two groups of relationships for weak solutions to generated Jacobian equations under proper assumptions on the generating functions and the domains, which are generalizations for the optimal transportation case and the standard Monge-Ampère case respectively. One group of weak solutions is Aleksandrov solution, Brenier solution and $ C $-viscosity solution. The other group of weak solutions is Trudinger solution and $ L^p $-viscosity solution.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.